Using a sharp knife, dice chicken into 1/3" thick pieces and place them in a large mixing bowl. If chicken breast is partially frozen, it will be a little bit easier to slice.
Into the mixing bowl, add remaining batter ingredients: 2 eggs, 1/3 cup mayonnaise, 1/3 cup flour, 1 1/3 cups shredded mozzarella, 1 1/2 Tbsp dill, 1/2 tsp salt, and 1/8 tsp black pepper, or season to taste. Stir the mixture until well combined.
Cover with plastic wrap and refrigerate for 2 hours or overnight to meld the flavors.
Heat a large non-stick pan over medium heat and add 2 Tbsp oil. Allow it to heat until shimmering.
Once the oil is hot, add the chicken mixture by heaping tablespoons and slightly flatten with a spoon.
Sauté uncovered for 3 to 4 minutes until golden brown, then flip and sauté for another 3 minutes on the second side.
Remove fritters and let them rest on paper towels. Repeat with remaining batter, adding more oil as necessary.
To make the aioli (if using), combine all the ingredients in a small bowl and stir until smooth.
